2023-2024 / SYST0017-1

Advanced topics in systems and control


26h Th, 26h Pr

Nombre de crédits

 Master : ingénieur civil biomédical, à finalité5 crédits 
 Master : ingénieur civil électricien, à finalité5 crédits 


Pierre Dauby, Guillaume Drion

Langue(s) de l'unité d'enseignement

Langue anglaise

Organisation et évaluation

Enseignement au premier quadrimestre, examen en janvier


Horaire en ligne

Unités d'enseignement prérequises et corequises

Les unités prérequises ou corequises sont présentées au sein de chaque programme

Contenus de l'unité d'enseignement

The course is an introduction to the dynamics of excitable systems, with a particular focus on neuronal excitability at the cellular and network levels.

The course will cover basic dynamical properties of neurons, which include

  • Excitability and spiking activity
  • Type I and Type II excitability
  • Rest-spike bistability
  • Bursting
At the network level, rate models will be introduced and developed, with several applications. 

  • Dendritic and axonal propagation
  • Models of synapse
  • Population dynamics : rates models, neural mass models, neural fields models
  • Possible applications: decision making, associative memory, learning, visual hallucinations, wake-sleep cycle...
In addition, the course will use neuronal dynamics as a case study to introduce general concepts of linear and nonlinear dynamics, which include

  • stability of equilibria and limit cycles
  • phase portrait analysis
  • bifurcations of fixed points and limit cycles
  • singularities
  • space-time behaviour, space-time pattern formation
  • etc.

Acquis d'apprentissage (objectifs d'apprentissage) de l'unité d'enseignement

At the end of this course, the student will have a good understanding of the mechanisms underlying neuronal dynamics and neuromodulation. He/she will master the mathematical concepts and techniques required to study these dynamics: phase portrait analysis, trajectory simulation, fixed point computation, stability analysis, bifurcation diagrams, space-time behaviour, etc. In addition, the student will be able to use the relevant tools on computer (Julia).

Ce cours contribue aux acquis d'apprentissage I.1, I.2, II.1, II.2, II.3, III.1, III.2, IV.1, VI.1, VII.1, VII.2, VII.3, VII.4, VII.5 du programme d'ingénieur civil en génie biomédical.

Ce cours contribue aux acquis d'apprentissage I.1, I.2, II.1, II.2, II.3, III.1, III.2, IV.1, IV.8, VI.1, VII.1, VII.2, VII.3, VII.4, VII.5 du programme d'ingénieur civil électricien.

Savoirs et compétences prérequis

SYST0002-1 ou un cours équivalent

Activités d'apprentissage prévues et méthodes d'enseignement

For the first part of the course on cellular dynamics, the course is based on 2h tutorials on Julia notebooks followed by 2h ex-cathedra lectures on theoretical concepts. Active student participation is required during the tutorials. The second part on populations dynamics will consists in ex-cathedra lectures and a project (report on a scientific paper, with associated computer modelling).

Mode d'enseignement (présentiel, à distance, hybride)

Cours en présentiel.

Lectures recommandées ou obligatoires et notes de cours

Recommanded readings:

'Nonlinear Dynamics and Chaos: with applications to Physics, Biology, Chemistry and Engineering', Steven H. Strogatz, Perseus Publishing, 2001.

'Dynamical Systems in Neuroscience: the Geometry of Excitability and Bursting', Eugene M. Izhikevich, The MIT Press, 20086.

'Neuronal Dynamics. From singles neurons to networks and models of cognition', Wulfram Gerstner, Werner M. Kistler, Richard Naud, Liam Paninski, Cambridge University Press, 2014. 

Modalités d'évaluation et critères

Examen(s) en session

Toutes sessions confondues

- En présentiel

évaluation écrite

Travail à rendre - rapport

Evaluation continue

Explications complémentaires:

Explications complémentaires:

Julia notebooks will be evaluated throughout the year; the project report is evaluated only in the first session (the mark obtained is automatically transferred to the second session); a written exam is organised during both sessions. (Note that the timely submission of the reports associated with the hands-on work is a condition for participating in the written examination.)


Remarques organisationnelles et modifications principales apportées au cours

Additional information and lecture notes will be provided on eCampus. 


G. Drion (gdrion@uliege.be, Bldg. B28, office I140)

P.C. Dauby (PC.Dauby@uliege.be, Bldg. B5a, office 2/57) 

Association d'un ou plusieurs MOOCs